Using Langevin dynamics simulations, we examine the effect of chain sequence on the thermodynamics and kinetics of heteropolymer collapse. We employ a bead-spring model with two monomer types: one for which the solvent is good and the other, poor. Steady-state results indicate that the collapse of large block chains occurs over a wide temperature range. The collapsed state is well-defined in the case of small block chains and consists of a string of unimolecular micelles. We follow the kinetics of collapse by measuring the number of clusters N-c and the radius of gyration R-g over time, starting from an instant temperature quench. Our results are in agreement with the well-known model of collapse in which cluster formation occurs rapidly and is followed by cluster aggregation. The details of this cluster formation and coalescence mechanism differ strongly depending on block size, and this in turn is found to affect the overall rate of collapse.